A landscaping company claims that 90% of the trees they plant survive (defined as being still alive one year from planting). If a tree does not survive, the company will replace the tree with a new one. A homeowner will have 5 trees planted in his yard by this landscaping company. Consider these 5 trees to be a random sample of all trees planted by this company. If the company's claim is correct, what is the probability that all 5 of the trees will survive? A) (0.1)⁵ B) (0.9)⁵ C) (0.1) + (0.1) + (0.1) + (0.1) + (0.1) = 0.5 D) (0.9)

Question

Quizplus · Accepted Answer

The probability that each tree survives is 0.9. Since the trees are planted independently, the probability that all 5 trees survive is $0.9^5$.

A Landscaping Company Claims That 90% of the Trees They